Ford Motor Co. is considering significant changes to the auto maker’s senior leadership team amid tension among top executives, dissatisfaction with the stock price and a drive to clarify the company’s strategy, according to people familiar with the situation.

The moves could include a shuffling of executives who were hired or rose to prominence during the tenure of Alan Mulally, the company’s chief executive for eight years ending in 2014. The current management team has been retooling the company to better prepare for...